Research article

$\mathcal{A}$-valued norm parallelism in Hilbert $\mathcal{A}$-modules

  • Received: 10 February 2019 Accepted: 14 May 2019 Published: 29 May 2019
  • MSC : 46L08, 46L05

  • We define the concept of $\mathcal{A}$-valued norm parallelism in a Hilbert $\mathcal{A}$-module, and then we investigate some properties of this notion and present some characterizations of $\mathcal{A}$-valued norm parallelism in a Hilbert $\mathcal{A}$-module. We also show that if $X$ and $Y$ are two inner product $\mathcal{A}$-modules and $T:X \to Y $ is a linear map such that $|Tx| = |x|$, then $T$ preserves $\mathcal{A}$-valued norm parallelism in both directions.

    Citation: Ali Khalili, Maryam Amyari. $\mathcal{A}$-valued norm parallelism in Hilbert $\mathcal{A}$-modules[J]. AIMS Mathematics, 2019, 4(3): 527-533. doi: 10.3934/math.2019.3.527

    Related Papers:

  • We define the concept of $\mathcal{A}$-valued norm parallelism in a Hilbert $\mathcal{A}$-module, and then we investigate some properties of this notion and present some characterizations of $\mathcal{A}$-valued norm parallelism in a Hilbert $\mathcal{A}$-module. We also show that if $X$ and $Y$ are two inner product $\mathcal{A}$-modules and $T:X \to Y $ is a linear map such that $|Tx| = |x|$, then $T$ preserves $\mathcal{A}$-valued norm parallelism in both directions.


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  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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